During the last year, we have been using statistical-mechanical analysis and computer simulations to study the protein-folding problem. Our research made significant progress in identifying the correct approaches for studying the folding problem and in understanding the basic physics of protein folding. We carried out detailed analyses of the statistical mechanics of the two prevailing protein models. This analysis was made possible by our newly developed compuation procedures which can determine accurately the density of states of the different protein models. Such information allows us to characterize the thermodynamics and folding kinetics of the protein models quantitatively. We found that, even though the two types of models have similar thermodynamic character, the origins of folding cooperativity of the models are different. The contact-based cubic-lattice chain model lacks the typical long-range cooperativity among locally structured units in real proteins, but the other model describes such behavior well. The two types of models have different folding kinetics; their densities of states, thereby their energy landscapes, are different. By identifying the differences among two prevailing protein models and removing the unphysical features in the theoretical picture of protein folding, we sharpen our understanding about the protein folding problem. Our results lead to a more realistic molecular mechanism for the cooperative folding of proteins, and we obtain more definite information about what kind of folding behavior will arise with certain types of interactions and how to combine the various intramolecular interactions into a specific force field for folding proteins. We are currently building upon the progress of our most recent research to develop a general protein model with a realistic force field for predicting the native structure of real proteins and for designing new proteins with novel properties.